1. Field of the Invention PA1 2. Discussion of the Related Art PA1 E is the Young modulus, PA1 .alpha. is the expansion coefficient of the material of the resonator beams, PA1 l is the width of the resonator beams, PA1 .DELTA.T is the difference of temperature, PA1 .DELTA.x is the motion of the seismic mass M, PA1 e is the thickness of the resonator beams, and PA1 L is the length of the resonator beams.
The present invention relates to microaccelerometers of the type formed from a plate of a material such as quartz or silicon etched so as to delineate a seismic mass maintained on a frame by hangers and connected to this frame by beams constituting resonators.
Such a microaccelerometer is disclosed in U.S. Pat. No. 5,261,277 assigned to the applicant. The U.S. patent discloses a microaccelerometer constituted from a thin plate of a material such as silicon or quartz that is sandwiched between two plates constituting upper and lower covers, and the connection between a moving mass formed in the central plate and the frame of this central plate by hangers and by beams forming resonators. The resonators are capacitively coupled to metallizations formed on either one of the cover plates.
FIGS. 1A-1C schematically illustrate a structure of a moving mass M, hanging legs S1 and S2 and resonator beams R1 and R2. The structure is not identical to the structure of the above-mentioned U.S. patent and is simplified to emphasize the problem that the present invention aims to solve. The hanging legs S1 and S2 extend along an axis y and the resonator beams R1 and R2 extend along an axis x perpendicular to axis y. The legs S1 and S2 are designed in order to have a high rigidity along axis z perpendicular to plane x, y and to be very flexible along the axis direction x. Thus, when subjected to an acceleration oriented along axis x, the mass M can move slightly along this direction, which causes the resonating beam R1 to be expanded and the resonating beam R2 to be compressed. These stresses on the resonator beams modify their resonance frequencies, the frequency variation characterizing the acceleration.
FIG. 1B is a schematic cross-sectional view along line BB of FIG. 1A representing the assembly of an accelerometer plate according to the present invention. The seismic mass M is etched from an intermediate plate which comprises a frame 10 sandwiched between two plates forming the protection cover plates 11 and 12. Plate 11 comprises electrical conductors arranged so as to excite and to detect the resonance of the resonators R1 and R2, which are metallized or conductive (refer to U.S. Pat. No. 5,261,277).
The effect of an inhomogeneous temperature inside the chamber accommodating the accelerometer will now be described with relation to FIG. 1C. More particularly, it is assumed that the resonator beam R1 is at a temperature higher by .DELTA.T than the resonator beam R2. Then, the resonator beam R1 tends to extend and, in response to the reaction of the resonator beam R2, the beam R1 is subjected to compression like the beam R2. Thus, the seismic mass M is subjected to the force F generated by the expansion of beam R1, to the reaction force F' of beam R2 and to the return forces F1 and F2 of the hanging legs S1 and S2. It is clear that the torsion forces F1 and F2 are negligible as compared with the compression forces F and F'. Thus, by a first approximation, at equilibrium, F+F'=0.
Force F is expressed by: EQU F=E(.alpha.L.DELTA.T-.DELTA.x)el/L,
where
Force F' is expressed by: EQU F'=-Eel/L.DELTA.x.
F+F'=0 leads to: EQU .DELTA.x=.alpha.l.DELTA.T/2,
and EQU F=Eel.alpha..DELTA.T/2
By examining the consequences of temperature variations on the resonance frequency f of the resonators, the equation for the first resonator is EQU .delta.f=KF,
and for the second resonator EQU .delta.f'=-K'F'.apprxeq.-K'F=-(K+.DELTA.K)F.
It is assumed above that the ratio between the frequency variation and the force is not strictly identical for the two resonators. Indeed, the structures of the two resonators are unavoidably dissimilar. This leads to .DELTA.f-.delta.f'=.DELTA.KF. In addition, it is known that .delta.f-.delta.f'=KM.delta..gamma., where M designates the mass of the seismic mass. Thus, the equivalent acceleration which is measured in the absence of acceleration is .delta..gamma., but when the temperature of one of the resonators differs from the other, the acceleration is EQU .delta..gamma.=(.DELTA.K/K)(F/M) (.DELTA.K/K)Eel.alpha..DELTA.T/2M.(1)
Consider an example in the case where the seismic mass and the resonators are made of silicon. Then E=1.7.times.10.sup.11 N/m.sup.2, .alpha.=2.6.times.10.sup.-6 /.degree.C. The case where e=20 .mu.m, l=60 .mu.m, M=6.3.times.10.sup.-6 kg, is also considered. Then, if .DELTA.K/K is approximately 5% (which corresponds to usual fabrication allowances), one obtains for a variation .DELTA.T=1/1000/.degree.C., .delta..gamma.=200 .mu.g (where g designates the gravity acceleration).
In practice, differences up to some hundredths of a degree between the resonator beams are far from being impossible. This leads to errors in the acceleration measurements of approximately 2 mg. Such errors are not negligible because an accelerometer of the considered type can be used to reach precisions better than 1 mg.